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The reason stated in Anagarika Dharmapala's wikipedia page for his split with the Theosophical society is that he was against the idea of a universal religion that the Theosophists were aiming at.

Dharmapala eventually broke with Olcott and the Theosophists because of Olcott's stance on universal religion. One of the important factors in his rejection of theosophy centered on this issue of universalism; the price of Buddhism being assimilated
into a non-Buddhist model of truth was ultimately too high for
him."Dharmapala stated that Theosophy was "only consolidating
Krishna worship." "To say that all religions have a common
foundation only shows the ignorance of the speaker; Dharma alone is
supreme to the Buddhist".

Dharmapala broke with Olcott in 1904 when the latter showed disrespect toward the relic of the Buddha's tooth, one of the most sacred relics of the Buddha worshipped in Sri Lanka.

The author cites Return to Righteousness: A Collection of Speeches, Essays, and Letters of the Anagarika Dharmapala as the original source for this and quotes the following phrase from this book in a footnote,

Col. Olcott insulted the feelings of the Buddhists by showing disrespect to the Tooth Relic, a copy of which he had placed under the shelf.

After the split I don't think there was enough time for something significant to happen, because Henry Steel Olcott died on 1907.